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::1 is the compressed format IPV6 loopback address 0:0:0:0:0:0:0:1. It is the equivalent of the IPV4 address 127.0. 0.1. If you are trying to find your machines public IP address then you can use whatsmyip.org.
Localhost is the default name of the computer you are working on. The term is a pseudo name for 127.0. 0.1, the IP address of the local computer. This IP address allows the machine to connect to and communicate with itself.
The IP address is a 32-bit number that uniquely identifies a network interface on a machine. An IP address is typically written in decimal digits, formatted as four 8-bit fields separated by periods. Each 8-bit field represents a byte of the IP address.
An IP address is a string of numbers separated by periods. IP addresses are expressed as a set of four numbers — an example address might be 192.158. 1.38. Each number in the set can range from 0 to 255. So, the full IP addressing range goes from 0.0.
::1 is the loopback address in IPv6. Think of it as the IPv6 version of 127.0.0.1.
See http://en.wikipedia.org/wiki/Localhost
Just to add little more info to it, in IPv6 loopback address is represented as 127 zeroes followed by a 1 i.e (0000... 127 times..1). It's representation should have been like this -> 0000:0000:0000:0000:0000:0000:0000:0001 but we have some short form representation for this. If there are all zeroes in a single block you can replace it by single 0. So it becomes -> 0:0:0:0:0:0:0:0001. Again we can see that we have runs of zeroes, they can be eliminated and we get -> ::0001 -> ::1 .
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